dedekind::algebra::IsArithmeticAdditiveGroup Concept Reference

The ℤ-deal: a carrier that is an additive group AND whose group structure agrees with the standard C++ +, -, unary - operators. More...

Concept definition

template<typename T>
concept dedekind::algebra::IsArithmeticAdditiveGroup = 
    dedekind::category::IsGroup<T, std::plus<T>> &&
    IsAlgebra<T, std::plus<T>> && HasGroupOperatorsAdd<T>

Detailed Description

The ℤ-deal: a carrier that is an additive group AND whose group structure agrees with the standard C++ +, -, unary - operators.

Where the concepts meet for the additive-group surface, parallel to IsArithmeticRing (:ring) for the ring surface. IsArithmeticAdditiveGroup<T> requires both:

• category::IsGroup<T, std::plus<T>> + IsAlgebra — the strict categorical additive-group proof (type level) under the canonical + functor, with std::semiregular + closure;
• HasGroupOperatorsAdd<T> — the literal C++ operators +, -, unary - close strictly on T.

Canonical inhabitant: the project's exact ℤ carrier numbers::Z1 = sets::SignedExtensionalCardinal<>. Modular carriers also fire (e.g. unsigned int): the modular wrap Z/2^N Z is a finite additive group and the literal operators close strictly.

Introduced under #394 as the user-requested ℤ-deal.